Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON):

Solution:
from sys import maxint, exit

num_rows, num_cols = map(int, raw_input().split(' '))

playing_field_rows = []

for i in xrange(num_rows):
	playing_field_rows.append(map(int, raw_input().split(' ')))

moves = []

# Remove surplises from rows

row_maxes = []

for row in playing_field_rows:
	row_maxes.append(max(row))

smallest_row_max = min(row_maxes)

for i_row in xrange(num_rows):
	surplus = row_maxes[i_row] - smallest_row_max

	for j in xrange(surplus):
		moves.append("row %d" % (i_row + 1, ))

	if surplus != 0:
		playing_field_rows[i_row] = map(lambda x: x - surplus, playing_field_rows[i_row])

# Remove surpluses from columns

def get_column(i_col, rows):
	return [rows[j][i_col] for j in xrange(num_rows)]

def map_column(f, i_col, rows):
	mapped_column = map(f, get_column(i_col, rows))

	for i in xrange(num_rows):
		rows[i][i_col] = mapped_column[i]

col_maxes = []

for column in [get_column(i, playing_field_rows) for i in xrange(num_cols)]:
	col_maxes.append(max(column))

smallest_col_max = min(col_maxes)

for i_col in xrange(num_cols):
	surplus = col_maxes[i_col] - smallest_col_max

	for j in xrange(surplus):
		moves.append("col %d" % (i_col + 1, ))

	if surplus != 0:
		map_column(lambda x: x - surplus, i_col, playing_field_rows)

# At this point all cells must have the same and non-negative value

common_value = playing_field_rows[0][0]

if common_value < 0:
	print -1
	exit(0)

for i_row in xrange(num_rows):
	for i_col in xrange(num_cols):
		current_cell = playing_field_rows[i_row][i_col]

		if current_cell != common_value:
			print -1
			exit(0)

if num_rows <= num_cols:
	for i_row in xrange(num_rows):
		for j in xrange(common_value):
			moves.append("row %d" % (i_row + 1, ))
else:
	for i_col in xrange(num_cols):
		for j in xrange(common_value):
			moves.append("col %d" % (i_col + 1, ))

print len(moves)

for move in moves:
	print move